Discussion
A telephone line normally has a bandwidth of 3000 Hz assigned for data communications. The signal-to-noise ratio is usually 3162. Then the channel capacity for this channel is :
Answer: A
The channel capacity is 34,860 bps.
By Shannon's formula for a noisy channel:
\[ \begin{aligned} C &= B \log_{2}(1 + \text{SNR}) \\ &= 3000 \log_{2}(1 + 3162) \\ &= 3000 \times 11.62 \approx 34{,}860 \text{ bps} \end{aligned} \]
(More precise logarithms give about 34,880 bps; the textbook value, from Forouzan, rounds the logarithm to 11.62.) Option (C), 11.62, is the logarithm alone without multiplying by the bandwidth. The other values do not come from the formula.
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